Homomorphisms between Weyl modules for SL_3(k)

Details Homomorphisms between Weyl modules for SL_3(k) Homomorphisms between Weyl modules for SL_3(k)

2005-08-26

arxiv.org/abs/math/0508520v1

Mathematics

Representation Theory

41 pages, 2 colour figures, 25 black and white figures

Scientific paper

We classify all homomorphisms between Weyl modules for SL_3(k) when k is an algebraically closed field of characteristic at least three, and show that the Hom-spaces are all at most one-dimensional. As a corollary we obtain all homomorphisms between Specht modules for the symmetric group when the labelling partitions have at most three parts and the prime is at least three. We conclude by showing how a result of Fayers and Lyle on Hom-spaces for Specht modules is related to earlier work of Donkin for algebraic groups.

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